De. Edmunds et al., DOUBLE EXPONENTIAL INTEGRABILITY OF CONVOLUTION-OPERATORS IN GENERALIZED LORENTZ-ZYGMUND SPACES, Indiana University mathematics journal, 44(1), 1995, pp. 19-43
This paper provides estimates for an appropriate norm of the convoluti
on of a function in a Lorentz space with one in a generalized Lorentz-
Zygmund space. As a corollary, it is shown that the Riesz potential of
a function in an appropriate generalized Lorentz-Zygmund space satisf
ies a 'double exponential' integrability condition. The results extend
those of Brezis-Wainger on the convolution of functions in Lorentz sp
aces which lead to exponential integrability.